Office: South 326A

Telephone: 245-5403

Office Hours: Monday 5-6p in South 309, Tuesday 1-2p in South 309. Wednesday 12:30-1:20p in South 309, Thursday 8-9p in South

Email Address: Johannes@Geneseo.edu

Web-page: http://www.geneseo.edu/~johannes

- to develop familiarity and comfort with the language of more formal mathematics and proofs before taking upper division mathematics coursework
- to learn and justify several techniques for counting

Because the text is exceptionally accessible, we will structure class-time more as an interactive discussion of the reading than lecture. For each class day there is an assigned reading. Read and take notes on the section before coming to class. In addition to the reading, there are also indicated exercises to check that you understood the reading. When we complete questions from the reading we will discuss those indicated exercises during the class discussion.

- Apply the logical structure of proofs and work symbolically with connectives and quantifiers to produce logically valid, correct and clear arguments,
- Perform set operations on finite and infinite collections of sets and be familiar with properties of set operations,
- Determine equivalence relations on sets and equivalence classes,
- Work with functions and in particular bijections, direct and inverse images and inverse functions,
- Construct direct and indirect proofs and proofs by induction and determine the appropriateness of each type in a particular setting. Analyze and critique proofs with respect to logic and correctness, and
- Unravel abstract definitions, create intuition-forming examples or counterexamples, and prove conjectures.
- Write solutions to problems and proofs of theorems that meet rigorous standards based on content, organization and coherence, argument and support, and style and mechanics.

Homework (6) 5% each

Quizzes (3) 5% each

Colloquium Report (1) 5%

In-class exams (2) 15% each

Final exam (1) 20%

0 - missing or plagiarised question

1 - question copied

2 - partial question

3 - completed question (with some solution)

4 - completed question correctly and well-written

Each entire homework set will then be graded on a 90-80-70-60% (decile) scale. Late items will not be accepted, as solutions will be posted immediately. Homework will be returned on the following class day. Please feel free to discuss any homework with me outside of class or during review.

100 - 80% A

79 - 60% B

59 - 40% C

39 - 20% D

below 20% E

For your interpretive convenience, I will also give you an exam grade converted into the decile scale. The exams will be challenging and will require thought and creativity. They will not include filler questions (hence the full usage of the grading scale).

August 28

- September 11 Chapter I reading discussions

September 13 Chapter I homework due

September 18 Chapter I quiz taken

September 13-22 Chapter II reading discussions

September 25 Chapter II homework due

September 25-27 review Chapters I and II

September 29 In class exam covering Chapters I and II

October 2-16 Chapter III reading discussions

October 18 Chapter III homework due

October 23 Chapter III quiz taken

October 18-25 Chapter IV reading discussions

October 27 Chapter IV homework due

October 27 - 30 review Chapters III and IV

November 1 In class exam covering Chapters III and IV

November 3 -15 Chapter V reading discussions

November 17 Chapter V homework due

November 27 Chapter V quiz taken

November 17

- December 6 Chapter VII reading discussions

December 8 Chapter VII homework due

December 8-11 review Chapters V and VII, and course as whole

Friday, December 15 3:30-6:30p Final exam, first half covering chapters V and VII

second half covering course

Problem Sets:

Assignment for Chapter 1: To the student.1, 3.2, 3.6, 4.3, 4.10, 5.2, 5.12, 5.15, 5.23, 6.2, 6.4, 6.11, 7.8, 7.11

For example, this means that you must complete the second exercise in section 3. There is also a required exercise at the end of the "to the student" section.

Assignment for Chapter 2: 8.5, 8.12, 8.18, 9.2, 9.8, 10.3, 10.11, 11.5, 12.18, 12.21

Assignment for Chapter 3: 14.6, 14.13, 14.16, 15.6, 15.12, 15.15, 16.11, 16.13, 17.14, 17.23, 17.24, 17.33

Assignment for Chapter 4: 20.5, 20.7, 20.14, 22.9, 22.16 (valued as 6 questions)

Assignment for Chapter 5: 24.4, 24.8, 24.14, 24.16, 24.17, 24.20, 24.22, 25.9, 25.16, 26.4, 26.12, 27.2, 27.13

Assignment for Chapter 7: 35.4, 36.11, 36.15, 37.3, 37.14 (valued as 5 questions), supplemental E-primes.